Finite Group Databasebeta

← #14666076

Subgroups — #14666076

Order 2816.

446 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069867C211yesmaximal, characteristic, complemented
2#13067635C211yesmaximal, characteristic, complemented
3#13067533C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2826C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#400—21no—
10C11×#399C2211yescharacteristic
11C11×#397—21no—
12C11×#396—21no—
13C11×#394—21no—
14C11×#394—21no—
15C11×#392C2211yescharacteristic
16C11×#386—21no—
17C11×#385C2211yescharacteristic
18#10622830—21no—
19#10622826—21no—
20#10622581—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×#4323—41no—
45#66983—21no—
46#66983—21no—
47C2×(C2×D11)⋊C4—41no—
48#66939—41no—
49#66935—41no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66896—41no—
57C11⋊#95—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—41no—
61#66872—41no—
62#66870—42no—
63#12137—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C2×D44—21no—
91C2×D44—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—81no—
100C11×C22⋊C4—81no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107#4323—82no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—82no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#2826D1111yescharacteristic, complemented
116#2044—111no—
117#1613—111no—
118#1595—111no—
119#1352—111no—
120#1343—111no—
121#1326—111no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11#12011yescharacteristic
134C23×C11#13511yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—81no—
140C22×D11—81no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—82no—
144D4×C11—82no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—81no—
166C22⋊D11—81no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C22⋊D11—81no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176D44—81no—
177D44—81no—
178C11⋊C8—81no—
179C11⋊C8—81no—
180#534—111no—
181#481—221no—
182#447—221no—
183C2×#99—221no—
184#400—21no—
185#399C2×D1111yescharacteristic
186#397—21no—
187#396—21no—
188#394—21no—
189#394—21no—
190#392C2×D1111yescharacteristic
191#386—21no—
192#386—221no—
193#385C2×D1111yescharacteristic
194#342—111no—
195#327—221no—
196#327—221no—
197#323—111no—
198#323—111no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11#44911yescharacteristic
216C22×C11#45411yescharacteristic
217C22×C11B(4,𝔽2)11yescharacteristic
218C2×D11—82no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—161no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230Dic11—81no—
231Dic11—161no—
232C22×D4—21no—
233C22×D4—221no—
234C22×D4C22⋊D1111yescharacteristic
235C23×C4C22⋊D1111yescharacteristic
236C2×D8—441no—
237#123—441no—
238#121—221no—
239#121—221no—
240#120—441no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—441no—
253C2×C22⋊C4C22⋊D1111yescharacteristic
254C2×C22⋊C4C22×D1111yescharacteristic
255#106—441no—
256#102—441no—
257#102—441no—
258#99—442no—
259C22⋊C8—221no—
260C22⋊C8—221no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—441no—
266#95C22⋊D1111yescharacteristic
267#95C22⋊D1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—41no—
271C2×C11—41no—
272C2×C11—161no—
273C2×C11#159711yescharacteristic
274C2×C11#220011yescharacteristic
275C2×C11#220011yescharacteristic
276D11—161no—
277C24—21no—
278C24—221no—
279C24C2×C22⋊D1111yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—81no—
284C2×D4—81no—
285C2×D4—81no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—81no—
301C22×C4—221no—
302C22×C4—441no—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305D8—882no—
306C2×C8—441no—
307C2×C8—441no—
308C4⋊C4—41no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—81no—
319C22⋊C4—81no—
320C22⋊C4—81no—
321C22⋊C4—81no—
322C22⋊C4—81no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—882no—
328C11#1213711yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23—881no—
344C23—881no—
345C23#6700211yescharacteristic
346C23#6700311yescharacteristic
347C23#6700611yescharacteristic
348D4—42no—
349D4—81no—
350D4—82no—
351D4—82no—
352D4—881no—
353D4—881no—
354D4—881no—
355D4—881no—
356D4—881no—
357D4—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—881no—
385C8—881no—
386C8—881no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—882no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22—1761no—
408C22#1062285111yescharacteristic
409C22#1062285711yescharacteristic
410C22#1062285811yescharacteristic
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—881no—
419C4—1761no—
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2—161no—
425C2—1761no—
426C2#1306754511yescharacteristic
427C2#1307062311yescharacteristic
428C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2826C2
socleC22×C11B(4,𝔽2)
prime radical#13067533C2
hypercenter#2826D11
hypocenterC11#12137
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2826

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13069867C2semidirect
2. #13067635C2semidirect
4. #13066640C2semidirect
5. #13066613C2semidirect
6. #13066564C2semidirect
7. C11×#2826C2semidirect
115. #2826D11semidirect
328. C11#12137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130698672
#130676352
#130675332
#130666402
#130666132
#130665642
C11×#28262
#1213711